A homotopy algorithm for solving coupled riccati equations

Abstract

Abstract Many applications of optimization theory require the solution of a set of coupled Riccati equations. In multi‐person‐games problems, the players' decision for the Nash equilibrium depend on Riccati equations coupled through their quadratic terms. Another example is provided by linear‐quadratic control. When the system is subject to sudden and random changes in parameter values, the optimal feedback is computed from the solution of Riccati equations coupled through their weighting terms. After recalling the principle of homotopy methods, it is shown how it generates a new and efficient algorithm for this class of problem. An illustrative example is given.